Linear analogs number

Compared to a linear chain of the same number of units, a branched chain is more compact. As a result, the impact of branching on the size of a polymer chain is to decrease the mean-square radius as branching increases. To assess the decrease in size because of branching, the mean-square radius of a branched polymer is compared to the size of a linear analog of identical molecular weight. Quantitatively, this was defined by Zimm and Stockmayer with the following branching or contraction factor ... 

Other macromolecular architectures, such as linear polymers, and any comparisons that have been made were performed with polydisperse samples of significantly different repeat unit structure. For example, the unique melt viscosity behavior of polyether dendrimers was compared with linear polystyrene and not with monodisperse linear analogs containing the same number of polyether repeat units based on 3,5-dihydroxybenzyl alcohol (2). Because of this, important issues, such as i) effect of the numerous chain end functional groups, ii) the effect of branching and, iii) the development of a well defined three-dimensional architecture cannot be addressed and the underlying reason for these inherent differences remains a mystery. 

Figure 4. Plot of absorbance maximum versus generation number for solvaotochromically labeled dendrimers and linear analogs.

Fig. 24 Three-dimensional representation of the critical surface calculated for blends of a branched polymer consisting of 1000 segments but differing in its degrees of branching / , with its linear analogs varying in the number of their segments. Phase separation may set in (depending on the composition of the blend) if Z falls below its critical value Zcrif The area of possible demixing is located below the critical surface [28]...

There are a number of examples of macromolecules with very complex structural features such as stars, dendrimers, hyperbranches, and crosslinks. Each of fliese classes of materials comes with its own advantages and disadvantages in terms of synthesis, processability, and properties. The crosslinked polymer 64 was prepared by the thermal copolymerization of ferrocenophanes. The swelling properties of the crosslinked polymers allowed for determination of the solubility parameter of the analogous linear homopolymer. The crosslinked polymers were foimd to possess increased thermal stabihty relative to their linear analoges. 

The miktoarm star block copolymers (Fig. 5.14b and d) exhibited morphologies quite different from those observed for their linear analogs. The TEM for the (PCL2)39-( -(PS2)6i miktoarm copolymer (where the subscripts outside the brackets indicate the composition in wt%, while the superscript denotes the number average molecular weight of the entire block copolymer), see Figure 5.14b, exhibits a cylindrical... 

A comparison of the physical properties of hyperbranched and dendritic macromolecules with linear polymers and the linear analogs of these 3-dimensional polymers is presented. It is found that thermal properties, such as glass transition temperature and degradation, are the same regardless of the macromolecular architecture but are very sensitive to the number and nature of chain end functional groups. However, other properties, such as solubility, melt viscosity, chemicd reactivity, intrinsic viscosity were found to be very dependent on the macromolecular architecture. 

Dendritic polymers exhibit very different properties compared with their linear analogs. For instance, they exhibit extremely high solubility in various organic solvents and low intrinsic viscosity in comparison to their linear analogs. These differences are probably a reflection of the large number of chain end functional groups as well as the influence of architectural differences [59]. 

The situation is similar for a linear curve fit, except that now the data set is two-dimensional and the number of degrees of freedom is reduced to (n — 2). The analogs of the one-dimensional variance )/( 1) the standard... 

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